You are designing a lathe motor, part of which consists of a uniform cylinder wh

Question

You are designing a lathe motor, part of which consists of a uniform cylinder whose mass is 110 kg and whose radius is 0.80 m that is mounted so that it turns without friction on its axis, which is fixed. The cylinder is driven by a belt that wraps around its perimeter and exerts a constant torque. At t = 0, the cylinder's angular velocity is zero. At t = 25 s, its angular speed is 550 rev/min.

(a) What is the magnitude of the cylinder's angular momentum at t = 25 s?
_____kg·m2/s

(b) At what rate is the angular momentum increasing?
_____kg·m2/s2

(c) What is the magnitude of the torque acting on the cylinder?
_____N·m

(d) What is the magnitude of the frictional force acting on the rim of the cylinder?
_____N

Explanation / Answer

m = 110 kg r = 0.80m t = 25 s

angular speed w = 550 rev/min

= 550 x 2 x3.14 / 60

= 57.6 rad/s

a) Angular momentum L = I.w

= 0.5 m r2 w

= 0.5 x 110 x 0.8 x 0.8 x 57.6

= 2027.52 Kgm2/s

b) rate = dL/dt = 2027.52 / 25

= 81.1 kg·m2/s2

c) Torque T = dL/dt = 2027.52/25

= 81.1 N-m

d) torque T = F.R

hence F = T/R = 81.1/0.8 = 101.4 N

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